Problem $3(30$ points$)$

A channel transitions from a width $(b_1=2(m))$ to a width $(b_2=1\mathrm{.}84(m)).$ The upstream

depth $y_1=0\mathrm{.}6m$ and the flowrate in the channel is $Q=2\frac{m^3}{s}.$

a$)$ Calculate the downstream depth $y_2.$

b$)$ Plot in schematic form the specific energy diagram that corresponds to this flow

situation.

c$)$ Further downstream the channel slopes gently and is made of material with a

Manning's $n=0\mathrm{.}02.$ Calculate the slope So of the channel.

d$)$ Further downstream we are planning to develop the conditions necessary to form a

hydraulic jump in order to kill kinetic energy. With everything else remaining the same

$(b_2,Q,n),$ we can accomplish this by increasing the bed slope. Calculate the slope

needed to create the conditions to form a hydraulic jump.